Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TLDR
In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.Abstract:
This report demonstrates theoretically and empirically that a greedy algorithm called
Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension
d given O(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.read more
Citations
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Journal ArticleDOI
Energy-Efficient ECG Compression on Wireless Biosensors via Minimal Coherence Sensing and Weighted $\ell_1$ Minimization Reconstruction
TL;DR: An energy-efficient compressed sensing (CS)-based approach for on-node ECG compression and a weighted ℓ1 minimization model derived by exploring the multisource prior knowledge in wavelet domain to minimize the data rate required for faithful reconstruction are presented.
Proceedings ArticleDOI
Iterative algorithms for compressed sensing with partially known support
TL;DR: Three iterative algorithms are modified to incorporate the known support in the recovery process of sparse or compressible signals with partially known support, showing improvement in their performance.
Journal ArticleDOI
Sparse Sensor Placement Optimization for Classification
TL;DR: A novel algorithm to solve sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems and performs computationally efficient classification with accuracy approaching that of classification using full-state data.
Journal ArticleDOI
Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme
Xianye Li,Xiangfeng Meng,Xiulun Yang,Yurong Wang,Yongkai Yin,Xiang Peng,Wenqi He,Guoyan Dong,Hongyi Chen +8 more
TL;DR: Theoretical analysis and numerical simulations validate the feasibility of the proposed multiple-image encryption method via lifting wavelet transform (LWT) and XOR operation, based on a row scanning compressive ghost imaging scheme.
Journal ArticleDOI
CCR: Clustering and Collaborative Representation for Fast Single Image Super-Resolution
TL;DR: This paper proposes an effective and fast single image super-resolution (SR) algorithm by combining clustering and collaborative representation that obtains compelling SR images quantitatively and qualitatively against many state-of-the-art methods.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.